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Simulation of Asymptotically AdS5 Spacetimes with a Generalized Harmonic Evolution Scheme

Jan, 2012

35 pages

Published in:

Phys.Rev.D 85 (2012) 084038

e-Print:

1201.2132 [hep-th]

DOI:

10.1103/PhysRevD.85.084038

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Abstract: (arXiv)

Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be described by the (t,r,\chi,\theta,\phi) spherical coordinates adapted to the R{\times}S3 boundary. We focus on solutions that preserve an SO(3) symmetry that acts to rotate the 2-spheres parametrized by \theta,\phi. In the boundary conformal field theory (CFT), the way in which this symmetry manifests itself hinges on the way we choose to embed Minkowski space in R{\times}S3. We present results from an ongoing study of prompt black hole formation via scalar field collapse, and explore the subsequent quasi-normal ringdown. Beginning with initial data characterized by highly distorted apparent horizon geometries, the metrics quickly evolve, via quasi-normal ringdown, to equilibrium static black hole solutions at late times. The lowest angular number quasi-normal modes are consistent with the linear modes previously found in perturbative studies, whereas the higher angular modes are a combination of linear modes and of harmonics arising from non-linear mode-coupling. We extract the stress energy tensor of the dual CFT on the boundary, and find that despite being highly inhomogeneous initially, it nevertheless evolves from the outset in a manner that is consistent with a thermalized N=4 SYM fluid. As a first step towards closer contact with relativistic heavy ion collision physics, we map this solution to a Minkowski piece of the R{\times}S3 boundary, and obtain a corresponding fluid flow in Minkowski space.

11.25.Tq
04.25.D-
12.38.Mh
field theory: conformal
space-time: anti-de Sitter
space: Minkowski
black hole: formation
field theory: scalar
gravitation: duality
black hole: static

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